A Topological Study of Textile Structures. Part II: Topological Invariants in Application to Textile Structures

TLDR

This paper is the second in a series on topological classification of textile structures, using knot theory invariants to resolve the classification problem. The study applies and develops numerical and polynomial invariants, including a new Kauffman‑type polynomial, to classify doubly‑periodic textile structures. The authors compute these invariants for simple doubly‑periodic interlaced, woven, and knitted textile structures. The resulting invariant values distinguish among these textile structures.

Abstract

This paper is the second in the series on topological classification of textile structures. The classification problem can be resolved with the aid of invariants used in knot theory for classification of knots and links. Various numerical and polynomial invariants are considered in application to textile structures. A new Kauffman-type polynomial invariant is constructed for doubly-periodic textile structures. The values of the numerical and polynomial invariants are calculated for some simplest doubly-periodic interlaced structures and for some woven and knitted textiles.